atomic collapse in graphene.pdf
TRANSCRIPT
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Atomic collapse in graphene
Andrey V. Shytov (BNL)Work done in collaboration with:
L.S. LevitovMIT
M.I. at!nel!on
"niver!ity o# Ni$%e&en'Netherland!
* Phys. Rev. Lett. 99, 236801; ibid. 99, 246802 (2007)
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Outline
1. Atomic collapse and Dirac vacuum reconstructionin high-energy physics
2. Charged impurities in graphene: manifestations of atomic
collapse a. ocal DO! "!#$% &. #ransport "conductivity% c. 'acuum polari(ation
). Conclusion
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*lectrons in graphene
+seudo-spin "su&lattice%
#,o su&lattices
!lo, &ut ultrarelativisticDirac fermions
Chirality conservation /0 no locali(ation "lein parado%
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3hy graphene4
5igh mo&ility tuna&le carrier density
inear spectrum /0 high 6uanti(ation energiesroom temperature mesoscopic physics
7eali(ation of relativistic 6uantum physics inta&le-top eperiments /0 unusual transportproperties
arge fine structure constant /0 strong field
regime inaccessi&le in high-energy physics
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Charged impurities
Dominant contri&ution to resistivity
"7+A screeningis not essential%
Nom!", #$%o&"'d (200)
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Charged impurities
Dominant contri&ution to resistivity
"7+A screeningis not essential%
Nom!", #$%o&"'d (200)
Any interesting non-linear effects444
8es Dirac vacuum reconstruction
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!ta&ility of AtomClassical physics: unsta&le
"energy is un&ounded%
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!ta&ility of AtomClassical physics: unsta&le
"energy is un&ounded%
9$: sta&le or&its (ero
point motion stops thecollapse
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!ta&ility of AtomClassical physics: unsta&le
"energy is un&ounded%
9$: sta&le or&its (ero
point motion stops thecollapse
7elativity: collapsing or&its
v c
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!ta&ility of AtomClassical physics: unsta&le
"energy is un&ounded%
9$: sta&le or&its (ero
point motion stops thecollapse
7elativity: collapsing or&its 7elativity ; 9$: 444
v c
4
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!ta&ility of AtomClassical physics: unsta&le
"energy is un&ounded%
9$: sta&le or&its (ero
point motion stops thecollapse
7elativity: collapsing or&its 7elativity ; 9$: Collapse4
v c 444
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Dirac = epler pro&lem
%i!"$ (1929)
3hat happens at> 0 1)?4
D / )
+art @ "> 1)?%
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Dirac = epler pro&lem
inite si(e of nucleus"regulari(ation%
!olution can &e continuedto > 0 1)?.
Pome!"&$h "&d mo!odi&sii (194)
+art @@ "1)? > 1?B%
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Atomic collapse:semiclassical picture
7elativistic particle may fallto the Coulom& center
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Atomic collapse:semiclassical picture
7elativistic particle may fallto the Coulom& center
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Dirac = epler pro&lem
inite si(e of nucleus"regulari(ation%
1! level merges intoDirac sea at > / 1?B
Pome!"&$h "&d mo!odi&sii (194)
> 0 1?B4
+art @@ "1)? > 1?B%
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Dirac = epler pro&lem
inite si(e of nucleus"regulari(ation%
!olution can &e continuedto > 0 1)?. 1! level merges
into hole continuum at> / 1?B
Pome!"&$h "&d mo!odi&sii (194)
> 0 1?B4
+art @@ "1)? > 1?B%
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Dirac = epler pro&lem+art @@@ "> 0 >c / 1?B%
+e!shtey&, e'dovi$h (1969)Po-ov (1970)
7esonant electron state in Dirac sea
!creening &y pair production4
9uasilocali(ed state
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Atomic collapse in graphene
o mass /0 no discrete states continuous
spectrum
$anifestations: 6uasistationary states resonances
!trong effects in vacuum polari(ation no cutoff at
Compton ,avelength
Can &e modeled &y charged impurities:
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Charged impurity in grapheneDirac e6uation:
Ansat(:
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#,o regimes
Critical value:
!u&critical:
!upercritical: Oscillations small r
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*act solution
!u&critical case:
!cale-invariant solution "depends only on kr%
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Density of states
!tanding ,aves
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Density of states
!tanding ,aves
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Density of states
!tanding ,aves
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9uasi-&ound states
#ype of carriers is reversed at small r
lein tunneling couples electron-lie states at small rto hole-lie states at large r
9
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9uasi-&ound states
Classical motion
9uanti(ation condition:
#ransparency:
*act result near criticality:
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#ransport
9uasi-&ound states sho, up as
ano resonances
Drude conductivity
!cattering phases "etracted from eact solution%
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'acuum polari(ation
7+A "$irlin et al%:
Eeneral form:
#homas-ermi "atsnelson%:
7+A and # give conflicting results ,hich is unusual
i d l l
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riedel sum rule
in "2BBF%:
#otal charge:
+hases etracted from eact solution:
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!u&rcritical case
7+A formula is valid.
umericall results:
Only deep states contri&ute
to polari(ation charge"confirmed &y a direct calculation%
e!ehov et "'/e"$t o!m'" o!
-o'"!i"tio& $h"!e
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!upercritical case
"only s-channel isovercritical%
#homas-ermi limit
7E flo, of the effective charge:
#he flo, terminates at finite distance:
#he charge of an overcritical impurity
is al,ays screened to the critical value.
Open questions:
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Open questions:
*citons4
*ffect of vacuum polari(ation on locali(ed states4
Other many-&ody effects4 ondo4
7ole of ,ater4 Capacitance4Eapped systems "&ilayers epitaial graphene%4
Conclusions:
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Conclusions:
#,o distinct regimes for Coulom& impurities:su&critical and supercritical
ocal DO!: 6uasilocali(ed states standing ,aves
ano-lie resonances in transport cross-sectionconductivity
!creening cloud in supercritical regime
!ignatures of atomic collapse can&e o&served.
Divalent and tri-valent impurities are needed"Ca 8& a Ed can &e intercalated e.g.
$cChesney et al "2BB?%%. Alternatively onecan use the charge on !#$ tip.